edit: financial companies, or any company when dealing with a financial or privacy breach usually needs to prove their innocence when they are attributed to allegedly causing financial loss (to varied extents depending on the situation).
This is an expectation from society in general. It may not seem fair or be legally required, but that's just the way it is.
Thats why I completely believe the posters here claiming this wouldn't be possible in a banks call centre. What I don't know is whether PayPal operates at the same standard.
When debating any issue, there is an implicit burden of proof on the person asserting a claim. The fallacy of an argument from ignorance occurs if, when a claim is challenged, the burden of proof is shifted to be on the challenger.
The burden of proof is a philosophical concept which extends into the legal domain. In fact, it's the only sane way to process assertions made by purportedly rational actors, it's hardly limited to 'social/legal' contexts.
But I'm not sure why you didn't go look this up in Wikipedia before you commented.
You are looking at this as a claim between the thief and PayPal. The thief made the claim, so the burden of proof is on the thief.
But that's not what's going on. PayPayl is asserting a claim that they are safe, and the other party is every potential customer of PayPal. The burden is on PayPal to convince us of their claim that they are safe, in light of the claim against them.
To me, it is credible that the thief got the information from PayPal. Between the thief and PayPal, I think the thief has little incentive to lie about where he got the information, but PayPal has high incentive to cover up.
We're concerned with figuring out what we think is most likely. You are correct that we have insufficient information to know with high confidence who is telling the truth, but if we are in a position to use PayPal, we have to make a judgement anyway. Further, not having enough information to know most things with high confidence is the common case; we usually have to make decisions based on imperfect information.
In such cases, we have to use the imperfect information available to us. Prejudices is one word for it; Bayesians call it our priors.
For the record, I actually think PayPal is a net-good. I think that most of the negative press they put up with is unwarranted, and is a result of people not understanding how they are allowed to use the service. In addition, I think most people do not appreciate that PayPal is much more tolerant than the alternative that was the only-game-in-town before PayPal, which were merchant accounts with banks.